Data driven evaluation and rejection of trained Gaussian process-based wireless mean and standard deviation models

Abstract

Disclosed are apparatus and methods for providing outputs; e.g., location estimates, based on trained Gaussian processes. A computing device can determine trained Gaussian processes related to wireless network signal strengths, where a particular trained Gaussian process is associated with one or more hyperparameters. The computing device can designate one or more hyperparameters. The computing device can determine a hyperparameter histogram for values of the designated hyperparameters of the trained Gaussian processes. The computing device can determine a candidate Gaussian process associated with one or more candidate hyperparameter value for the designated hyperparameters. The computing device can determine whether the candidate hyperparameter values are valid based on the hyperparameter histogram. The computing device can, after determining that the candidate hyperparameter values are valid, add the candidate Gaussian process to the trained Gaussian processes. The computing device can provide an estimated location output based on the trained Gaussian processes.

The invention claimed is: 
     
       1. A method, comprising:
 determining by a computing device a plurality of trained Gaussian processes related to signal strengths of wireless networks, wherein a particular trained Gaussian process in the plurality of trained Gaussian processes is associated with one or more hyperparameters; 
 determining by the computing device one or more designated hyperparameters of the one or more hyperparameters; 
 determining by the computing device a hyperparameter histogram of a plurality of values for the one or more designated hyperparameters, wherein one or more particular values in the plurality of values are one or more values for the one or more designated hyperparameters associated with a trained Gaussian process of the plurality of trained Gaussian processes, and wherein the hyperparameter histogram comprises a plurality of histogram bins; 
 after determining by the computing device the hyperparameter histogram, determining a candidate Gaussian process by the computing device, wherein the candidate Gaussian process is associated with one or more candidate hyperparameter values for the one or more designated hyperparameters, and wherein the one or more candidate hyperparameter values are associated with a candidate histogram bin of the plurality of histogram bins; 
 determining by the computing device whether the one or more candidate hyperparameter values are valid based on the hyperparameter histogram by:
 determining one or more mean values and one or more standard deviation values for the values of the one or more designated hyperparameters represented by the hyperparameter histogram, 
 determining whether the candidate histogram bin is an outlier histogram bin based on the one or more mean values and the one or more standard deviation values, and 
 after determining that the candidate histogram bin is not an outlier histogram bin, determining that the one or more candidate hyperparameter values are valid; 
 
 after determining by the computing device that the one or more candidate hyperparameter values are valid, adding by the computing device the candidate Gaussian process to the plurality of trained Gaussian processes; 
 receiving a request related to locating a mobile device at the computing device; 
 determining by the computing device an estimate of the location of the mobile device based on the plurality of trained Gaussian processes; 
 generating by the computing device an estimated location output that comprises the estimate of the location of the mobile device; and 
 providing the estimated location output using the computing device. 
 
     
     
       2. The method of  claim 1 , wherein determining whether the candidate histogram bin is an outlier histogram bin based on the one or more mean values and the one or more standard deviation values comprises:
 determining a first mean value and a first standard deviation value for a first designated hyperparameter represented by the hyperparameter histogram; 
 determining a first range of values for the first designated hyperparameter based on the first mean value and the first standard deviation value; 
 determining a first bin mean of the first designated hyperparameter for the candidate histogram bin; and 
 determining whether the candidate histogram bin is an outlier bin based on the first bin mean and the first range of values. 
 
     
     
       3. The method of  claim 2 , wherein determining whether the candidate histogram bin is an outlier bin based on the first bin mean and the first range of values comprises:
 determining whether the first bin mean is outside of the first range of values; and 
 after determining that the first bin mean is outside of the first range of values, determining that the candidate histogram is an outlier bin. 
 
     
     
       4. The method of  claim 1 , wherein a designated hyperparameter of the one or more designated hyperparameters is associated with an attenuation value of one or more signals of the wireless networks. 
     
     
       5. The method of  claim 1 , wherein a particular histogram bin of the plurality of histogram bins is associated with one or more ranges of values of the one or more designated hyperparameters. 
     
     
       6. The method of  claim 5 , wherein determining by the computing device whether the one or more candidate hyperparameter values are valid based on the hyperparameter histogram comprises:
 determining one or more candidate ranges of values associated with the candidate histogram bin of the plurality of histogram bins, wherein the one or more candidate ranges of values include the one or more candidate hyperparameter values; and 
 determining whether the one or more candidate hyperparameter values are valid based on a histogram count associated with the candidate histogram bin. 
 
     
     
       7. The method of  claim 6 , wherein the particular histogram bin is further associated with a range histogram count, wherein the range histogram count for the particular histogram bin is based on a number of trained Gaussian processes whose designated hyperparameter values are within the ranges of values of the one or more designated hyperparameters associated with the particular histogram bin, and wherein the histogram count associated with the candidate histogram bin is based on a range histogram count for the candidate histogram bin. 
     
     
       8. The method of  claim 6 , wherein determining by the computing device whether the one or more candidate hyperparameter values are valid based on the hyperparameter histogram comprises:
 after determining that the candidate histogram bin is an outlier histogram bin, determining that the one or more candidate hyperparameter values are not valid. 
 
     
     
       9. The method of  claim 1 , further comprising:
 determining by the computing device a second candidate Gaussian process, wherein the second candidate Gaussian process is associated with one or more second candidate hyperparameter values for the one or more designated hyperparameters; 
 determining by the computing device whether the one or more second candidate hyperparameter values are valid based on the hyperparameter histogram; and 
 after determining by the computing device that the one or more second candidate hyperparameter values are not valid, rejecting by the computing device the second candidate Gaussian process. 
 
     
     
       10. A computing device, comprising:
 one or more processors; and 
 one or more non-transitory computer readable media, configured to store at least computer-readable program instructions, wherein the instructions are configured to, upon execution by the one or more processors, cause the computing device to perform functions comprising:
 determining a plurality of trained Gaussian processes related to signal strengths of wireless networks, wherein a particular trained Gaussian process in the plurality of trained Gaussian processes is associated with one or more hyperparameters; 
 determining one or more designated hyperparameters of the one or more hyperparameters; 
 determining a hyperparameter histogram of a plurality of values of the one or more designated hyperparameters, wherein one or more particular values in the plurality of values are one or more values for the one or more designated hyperparameters associated with a trained Gaussian process of the plurality of trained Gaussian processes, and wherein the hyperparameter histogram comprises a plurality of histogram bins; 
 after determining the hyperparameter histogram, determining a candidate Gaussian process, wherein the candidate Gaussian process is associated with one or more candidate hyperparameter values for the one or more designated hyperparameters, and wherein the one or more candidate hyperparameter values are associated with a candidate histogram bin of the plurality of histogram bins; 
 determining whether the one or more candidate hyperparameter values are valid based on the hyperparameter histogram by:
 determining one or more mean values and one or more standard deviation values for the values of the one or more designated hyperparameters represented by the hyperparameter histogram, 
 determining whether the candidate histogram bin is an outlier histogram bin based on the one or more mean values and the one or more standard deviation values, and 
 after determining that the candidate histogram bin is not an outlier histogram bin, determining that the one or more candidate hyperparameter values are valid; 
 
 after determining that the one or more candidate hyperparameter values are valid, adding the candidate Gaussian process to the plurality of trained Gaussian processes; 
 receiving a request related to locating a mobile device; 
 determining an estimate of the location of the mobile device based on the plurality of trained Gaussian processes; 
 generating an estimated location output that comprises the estimate of the location of the mobile device; and 
 providing the estimated location output. 
 
 
     
     
       11. The computing device of  claim 10 , wherein determining whether the candidate histogram bin is an outlier histogram bin based on the one or more mean values and the one or more standard deviation values comprises:
 determining a first mean value and a first standard deviation value for a first designated hyperparameter represented by the hyperparameter histogram; 
 determining a first range of values for the first designated hyperparameter based on the first mean value and the first standard deviation value; 
 determining a first bin mean of the first designated hyperparameter for the candidate histogram bin; and 
 determining whether the candidate histogram bin is an outlier bin based on the first bin mean and the first range of values. 
 
     
     
       12. The computing device of  claim 11 , wherein determining whether the candidate histogram bin is an outlier bin based on the first bin mean and the first range of values comprises:
 determining whether the first bin mean is outside of the first range of values; and 
 after determining that the first bin mean is outside of the first range of values, determining that the candidate histogram is an outlier bin. 
 
     
     
       13. The computing device of  claim 10 , wherein a designated hyperparameter of the one or more designated hyperparameters is associated with an attenuation value of one or more signals of the wireless networks. 
     
     
       14. The computing device of  claim 10 , wherein a particular histogram bin of the plurality of histogram bins is associated with one or more ranges of values of the one or more designated hyperparameters. 
     
     
       15. The computing device of  claim 14 , wherein determining whether the one or more candidate hyperparameter values are valid based on the hyperparameter histogram comprises:
 determining one or more candidate ranges of values associated with the candidate histogram bin of the plurality of histogram bins, wherein the one or more candidate ranges of values include the one or more candidate hyperparameter values; and 
 determining whether the one or more candidate hyperparameter values are valid based on a histogram count associated with the candidate histogram bin. 
 
     
     
       16. The computing device of  claim 15 , wherein the particular histogram bin is further associated with a range histogram count, wherein the range histogram count for the particular histogram bin is based on a number of trained Gaussian processes whose designated hyperparameter values are within the ranges of values of the one or more designated hyperparameters associated with the particular histogram bin, and wherein the histogram count associated with the candidate histogram bin is based on a range histogram count for the candidate histogram bin. 
     
     
       17. The computing device of  claim 15 , wherein determining whether the one or more candidate hyperparameter values are valid based on the hyperparameter histogram comprises:
 after determining that the candidate histogram bin is an outlier histogram bin, determining that the one or more candidate hyperparameter values are not valid. 
 
     
     
       18. The computing device of  claim 10 , wherein the functions further comprise:
 determining a second candidate Gaussian process, wherein the second candidate Gaussian process is associated with one or more second candidate hyperparameter values for the one or more designated hyperparameters; 
 determining whether the one or more second candidate hyperparameter values are valid based on the hyperparameter histogram; and 
 after determining that the one or more second candidate hyperparameter values are not valid, rejecting the second candidate Gaussian process. 
 
     
     
       19. An article of manufacture including one or more non-transitory computer-readable storage media having instructions stored thereon that, in response to execution by one or more processors, cause the one or more processors to perform functions comprising:
 determining a plurality of trained Gaussian processes related to signal strengths of wireless networks, wherein a particular trained Gaussian process in the plurality of trained Gaussian processes is associated with one or more hyperparameters; 
 determining one or more designated hyperparameters of the one or more hyperparameters; 
 determining a hyperparameter histogram of a plurality of values for the one or more designated hyperparameters using the computing device, wherein one or more particular values in the plurality of values are one or more values for the one or more designated hyperparameters associated with a trained Gaussian process of the plurality of trained Gaussian processes, and wherein the hyperparameter histogram comprises a plurality of histogram bins; 
 after determining the hyperparameter histogram, determining a candidate Gaussian process, wherein the candidate Gaussian process is associated with one or more candidate hyperparameter values for the one or more designated hyperparameters, and wherein the one or more candidate hyperparameter values are associated with a candidate histogram bin of the plurality of histogram bins; 
 determining whether the one or more candidate hyperparameter values are valid based on the hyperparameter histogram by:
 determining one or more mean values and one or more standard deviation values for the values of the one or more designated hyperparameters represented by the hyperparameter histogram, 
 determining whether the candidate histogram bin is an outlier histogram bin based on the one or more mean values and the one or more standard deviation values, and 
 after determining that the candidate histogram bin is not an outlier histogram bin, determining that the one or more candidate hyperparameter values are valid; 
 
 after determining that the one or more candidate hyperparameter values are valid, adding the candidate Gaussian process to the plurality of trained Gaussian processes; 
 receiving a request related to locating a mobile device; 
 determining an estimate of the location of the mobile device based on the plurality of trained Gaussian processes; 
 generating an estimated location output that comprises the estimate of the location; and 
 providing the estimated location output. 
 
     
     
       20. The article of manufacture of  claim 19 , wherein determining whether the candidate histogram bin is an outlier histogram bin based on the one or more mean values and the one or more standard deviation values comprises:
 determining a first mean value and a first standard deviation value for a first designated hyperparameter represented by the hyperparameter histogram; 
 determining a first range of values for the first designated hyperparameter based on the first mean value and the first standard deviation value; 
 determining a first bin mean of the first designated hyperparameter for the candidate histogram bin; and 
 determining whether the candidate histogram bin is an outlier bin based on the first bin mean and the first range of values.